To compare the performance of the two ansatz we consider the instance-by-instance scatter plot where we compare the \(\langle \mathrm {BEST}_5 \rangle \)  results for QAOA vs QAMPA after the \(\mathtt {scanlast}\)  optimization.Note that we do not consider the runs that are required to discover the best performing angles but we directly report the metric computed on the corresponding \(F(\epsilon _k)\)  distribution. The figure indicates with cross symbols the metric value for each instance and with the round dots the median/standard deviation of the results for all the instance results associated to a given \(p\) . What is clear from the results shown in Figure REF  is that as \(p\)  increases both ansätze perform essentially the same for all tested sizes. This convergence is not surprising as for large \(p\)  QAOA and QAMPA for the same number of parameters could be interpreted as a Trotter-like approximation of the same unitary evolution [1]}. Similar results are observed also for different \(R\)  in the metric (including the common expectation value metric \(R=1\) ), indicating that the output distribution for the \(\epsilon _k\)  at the current sizes is smooth and monotonic.
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